What is the general solution for tan^5(x)=tan(x) ?

The general solution for tan^5(x)=tan(x) is x=pin,x=(3pi)/4+pin,x= pi/4+pin

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tan^5(x)=tan(x)

tan^{5} (x) = tan (x)

x = πn, x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

Solution steps

tan^{5} (x) = tan (x)

Solve by substitution

tan (x) = 0, tan (x) = i, tan (x) = - i, tan (x) = - 1, tan (x) = 1

tan (x) = 0 : x = πn

tan (x) = i :

No Solution

tan (x) = - i :

No Solution

tan (x) = - 1 : x = \frac{3 π}{4} + πn

tan (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

x = πn, x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

cos^{2} (x) - 3 cos (x) = - 2

2 cot (x) + 3 = 1

3 tan (θ) - 23 = 3

1 - 2 sin^{2} (x) = sin (x)

sin (2 θ) = 2 cos^{2} (θ)

What is the general solution for tan^5(x)=tan(x) ?
The general solution for tan^5(x)=tan(x) is x=pin,x=(3pi)/4+pin,x= pi/4+pin